(1) Field of the Invention
This invention relates to a surface profile measuring method and apparatus for measuring rugged surface profiles. More particularly, the invention relates to a technique of measuring surfaces in a non-contact mode by using white light.
(2) Description of the Related Art
Conventional apparatus of this type include a well-known surface profile measuring apparatus which employs a method of measuring, by means of white light interference, rugged profiles of precision products such as semiconductor wafers and glass substrates for liquid crystal displays.
As shown in FIG. 1, a conventional surface profile measuring apparatus comprises an interferometer, in which white light from a white light source 90 is directed through a first lens 91 to a half mirror 92. The white light reflected by the half mirror 92 is condensed by a second lens 93, and passes through a beam splitter 95 and irradiates an object surface 96 to be measured.
The beam splitter 95 of the interferometer divides the white light into a part that irradiates the object surface 96, and a part that irradiates a reference surface 94. The white light irradiating the reference surface 94 is reflected by a reflector 94a on the reference surface 94, and reaches the beam splitter 95 again. The white light having passed through the beam splitter 95 is reflected by the object surface 96, and reaches the beam splitter 95 again. The beam splitter 95 brings together, to the same path again, the white light reflected by the reference surface 94 and the white light reflected by the object surface 96. At this time, an interference phenomenon occurs, which corresponds to a difference between a distance L1 from the reference surface 94 to the beam splitter 95 and a distance L2 from the beam splitter 95 to the object surface 96. The white light with which the interference has occurred travels through the half mirror 92 and into a CCD camera 98.
The CCD camera 98 picks up an image of the object surface 96 along with the white light with which the interference has occurred. This construction includes a varying device, not shown, for vertically shifting a unit having the beam splitter 95. Such shifting of the beam splitter 95 varies the difference between distance L1 and distance L2, thereby increasing or decreasing the intensity of the white light incident on the CCD camera 98. When, for example, attention is directed to a particular location on the surface 96 within a region covered by the CCD camera 98, the beam splitter 95 is moved to vary the difference from distance L2 less than distance L1 to distance L2 greater than distance L1. By measuring the intensity of white light having interfered (hereinafter referred to simply as xe2x80x9cinterference lightxe2x80x9d) in the particular location, a waveform as shown in FIG. 2A, in theory, is obtained. A height in the particular location on the object surface may be derived from a peak position in the waveform of intensity variations of the interference light. The rugged profile of the surface is measured by determining heights in a plurality of locations in a similar way.
It is to be noted that actual data obtained by measuring the intensity of interference light are discrete as shown in FIG. 2B. It is necessary to derive a peak position in the waveform of intensity variations of the interference light from such data.
A method and apparatus for determining a peak position in a waveform are disclosed in U.S. Pat. No. 5,133,601, for example. In the method and apparatus disclosed therein, each discrete data as shown in FIG. 2B is squared to obtain data as shown in FIG. 2C. Subsequently, these data are smoothed into a waveform as shown in FIG. 2D. A height in a particular location is determined from a peak position of the smoothed waveform.
However, such prior method and apparatus have the following drawbacks.
In U.S. Pat. No. 5,133,601 noted above, a theoretical waveform as shown in FIG. 2A must be reproduced since a waveform with a peak position occurring at the height in a particular location is based on data obtained through actual measurements. That is, in order to measure, with sufficient precision, a height in a particular location on an object surface being measured, intensity values of the interference light in the particular location must be sampled so finely as to enable reproduction of a theoretical waveform.
As a result, an extended sampling time is required to acquire numerous intensity values, and hence a disadvantage of consuming a long time in measuring a surface profile. Further, a huge amount of data is acquired by the sampling, which requires an increased storage capacity for storing such data. This results in an increased cost of manufacturing the apparatus, and an extended computation time for processing the large amount of data, thereby further extending the time consumed in measuring the surface profile.
This invention has been made having regard to the state of the art noted above, and its object is to provide a surface profile measuring method and apparatus for measuring rugged profiles of object surfaces at a relatively high speed and with high precision by determining heights in particular locations with increased precision from a relatively small amount of data.
The above object is fulfilled, according to this invention, by a surface profile measuring method for measuring rugged profiles of object surfaces, wherein interference fringes are produced by varying a relative distance between an object surface and a reference surface while irradiating the two surfaces with white light from a white light source, variations in intensity value of interference light occurring at this time are measured for a plurality of particular locations on the object surface, and heights in the particular locations are derived from a group of interference light intensity values acquired from each particular location, the method comprising:
a first step of limiting a frequency band of the white light from the white light source to a particular frequency band;
a second step of varying the relative distance between the object surface and the reference surface irradiated with the white light in the particular frequency band;
a third step of acquiring a group of interference light intensity values which are successively collected from each of the particular locations on the object surface at sampling intervals corresponding to a bandwidth of the particular frequency band, the intensity values corresponding to variations in the interference fringes occurring with variations in the relative distance between the object surface and the reference surface;
a fourth step of estimating characteristic functions based on amplitude components of a theoretical waveform of intensity value variations derived from the group of interference light intensity values; and
a fifth step of determining a height in each of the particular locations based on a peak position of the characteristic functions estimated.
The frequency band of the white light from the white light source is limited to a particular frequency band, and the white light in the particular frequency band irradiates the object surface and the reference surface. Interference fringes are produced according to an optical path difference between the white light reflected by the object surface and the white light reflected by the reference surface.
At this time, the relative distance between the object surface and the reference surface is varied to vary the optical path difference, and hence the interference fringes. Interference light intensity values resulting from the variations in the interference fringes are successively collected from a particular location on the object surface at sampling intervals corresponding to a bandwidth of the particular frequency band. As a result, a minimum group of interference light intensity values based on the white light in the particular frequency band is acquired.
An ideal waveform of the intensity value variations of interference light in the particular location is derived from the group of interference light intensity values, and characteristic functions based on amplitude components of the waveform are estimated. In the ideal waveform of the intensity value variations of interference light, a high-frequency function appears to vibrate within a low-frequency function. The characteristic functions correspond only to the low-frequency functions extracted. The characteristic functions have a peak position substantially coinciding with a position where the ideal waveform of interference fringes is at a maximum amplitude. Thus, a height in the particular location is determined based on the peak position. The rugged profile of the object surface is measured by determining heights in a plurality of such particular locations.
As described above, the frequency band of white light is limited to a particular frequency band, and the intensity values of interference fringes are sampled from each particular location at intervals corresponding to the bandwidth of the particular frequency band. Consequently, the intensity values may be sampled at larger sampling intervals than in the prior art which employs sampling intervals by taking the entire frequency band into account.
The group of interference light intensity values acquired through the sampling is one resulting from the white light in the particular frequency band. Consequently, a theoretical waveform form of the intensity value variations of interference light may be derived from the group of interference light intensity values. The characteristic functions based on amplitude components of the theoretical waveform may also be determined with ease.
Further, since a height in a particular location is determined based on the peak position of the characteristic functions, the height in the particular location may be determined faster than and with no less precision than in the prior art where a peak position is derived from a waveform based on actual measurement data.
That is, height information may be obtained from a smaller amount of data and with higher precision than in the prior art. This feature allows a surface profile to be measured in a reduced time, and requires only a reduced storage capacity for storing data, whereby an apparatus may be manufactured at reduced cost.
In this invention, preferably, the third step is executed with the sampling intervals determined by dividing xcfx80 by the bandwidth of the particular frequency band.
The sampling intervals are determined based on a value obtained by dividing xcfx80 by the bandwidth of the particular frequency band. As a result, the group of interference light intensity values may be acquired, which is a minimum group of sampled values needed to reproduce the theoretical waveform of the intensity value variations of interference light based on the white light in the particular frequency.
Since the sampling intervals are determined based on a value obtained by dividing xcfx80 by the particular frequency band, the sampling intervals corresponding to the particular frequency band may be determined easily.
In this invention, preferably, the fourth step is executed to derive an average intensity value from the group of interference light intensity values, obtain adjusted values by subtracting the average intensity value from the intensity values, respectively, and obtain new functions, as the characteristic functions, by substituting the adjusted values into a formula representing amplitude components of a waveform substantially extending through the adjusted values.
An average intensity value is derived from the group of interference light intensity values to determine a value of a centerline of the waveform showing the variations in the intensity values of interference light. Adjusted values are obtained by subtracting the average intensity value from the respective intensity values. Thus, the adjusted values form a group of values showing a waveform distributed across the centerline. This group of values is used to estimate the characteristic functions. These characteristic functions have a peak position substantially coinciding with a position where the waveform of the intensity values of interference fringes is at a maximum amplitude. Thus, the height in the particular location may be determined based on the peak position.
Further, since the height in the particular location is determined based on the peak position of the characteristic functions, height information may be obtained from a smaller amount of data and with higher precision than in the prior art.
In another aspect of this invention, a surface profile measuring apparatus for measuring rugged profiles of object surfaces, comprises:
a white light source for emitting white light to irradiate an object surface and a reference surface;
a varying device for varying a relative distance between the object surface and the reference surface;
a frequency band limiting device for limiting a frequency band of the white light emitted from the white light source to a particular frequency band;
an image pickup device for picking up an image of the object surface along with variations in interference fringes occurring with the variations in the relative distance between the object surface and the reference surface irradiated with the white light;
a sampling device having a function for acquiring intensity values of interference light from a plurality of particular locations on the object surface imaged, the sampling device acquiring interference light intensity values successively from each of the particular locations at sampling intervals corresponding to a bandwidth of the particular frequency band, the intensity values corresponding to variations in the interference fringes occurring with the variations in the relative distance between the object surface and the reference surface caused by the varying device;
a storage device having a function for storing a group of interference light intensity values acquired by the sampling device from each of the particular locations, the storage device storing the group of interference light intensity values acquired at the sampling intervals; and
a computing device having a function for measuring the rugged profile of the object surface by deriving a height in each of the particular locations from the group of interference light intensity values stored in the storage device, the computing device estimating characteristic functions based on amplitude components of a theoretical waveform of intensity value variations derived from the group of interference light intensity values stored in the storage device, and determining the height in each of the particular locations based on a peak position of the characteristic functions estimated.
The white light source emits white light in a relatively broad frequency band. The frequency band limiting device limits the white light in that frequency band to a particular frequency band. As a result, the frequency band of the white light irradiating the object surface and the reference surface may be grasped. The varying device varies the relative distance between the object surface and the reference surface irradiated with the white light in the particular frequency band. The image pickup device picks up an image of the object surface along with interference fringes varying with an optical path difference between the white light reflected by the object surface and the white light reflected by the reference surface. This enables a grasp of how interference fringes are generated or varied according to the rugged profile of the object surface. The sampling device, in order to acquire the intensity values of interference light varying in a particular location on the object surface, successively collects the intensity values of interference fringes at sampling intervals corresponding to the bandwidth of the particular frequency band. In this way, the sampling device acquires a minimum number of intensity values of interference light based on the white light in the particular frequency band. The storage device successively receives the intensity values acquired by the sampling device, thereby storing a group of interference light intensity values for the particular location. The computing device derives a theoretical waveform of the intensity value variations of interference light for the particular location from the group of interference light intensity values, and estimates characteristic functions based on amplitude components of this waveform. Further, the computing device derives a height in the particular location on the object surface based on a peak position of the characteristic functions. The rugged profile of the object surface is measured by determining heights in a plurality of such particular locations on the object surface.